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Copyright and Use of This Thesis This Thesis Must Be Used in Accordance with the Provisions of the Copyright Act 1968 COPYRIGHT AND USE OF THIS THESIS This thesis must be used in accordance with the provisions of the Copyright Act 1968. Reproduction of material protected by copyright may be an infringement of copyright and copyright owners may be entitled to take legal action against persons who infringe their copyright. Section 51 (2) of the Copyright Act permits an authorized officer of a university library or archives to provide a copy (by communication or otherwise) of an unpublished thesis kept in the library or archives, to a person who satisfies the authorized officer that he or she requires the reproduction for the purposes of research or study. The Copyright Act grants the creator of a work a number of moral rights, specifically the right of attribution, the right against false attribution and the right of integrity. You may infringe the author’s moral rights if you: - fail to acknowledge the author of this thesis if you quote sections from the work - attribute this thesis to another author - subject this thesis to derogatory treatment which may prejudice the author’s reputation For further information contact the University’s Copyright Service. sydney.edu.au/copyright A study of scaling physics in a Polywell device Scott Cornish (SID: 306130319) School of Physics University of Sydney Australia A thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy (Research) 2016 Declaration of originality I certify that the work presented in this thesis was undertaken solely during my PhD candidature, and has not been presented for any other degree. I certify also that this thesis was written by myself, and that all external contributions and sources have been duly acknowledged. Signature of candidate: ............................................ Scott Cornish i Acknowledgements A PhD thesis is awarded to only one person however as John Donne reminds us “no man is a island”. Without the help of countless others the writing of this thesis would have not been possible. I would like to take this opportunity to extend my utmost gratitude to all of those involved in this great effort. My primary supervisor A/Proff Joe Khachan was and is a seriously smashing supervisor from whom I have learned innumerable technical skills and plasma physics knowledge. From Joe I also learned the most important lesson of my own limitations as an individual physicist and the value of collaboration with others. I will always consider you as a friend and fellow colleague in the pursuit of truth and fusion energy. I have always enjoyed our conversations and I hope that I will be able to carry the torch for the Polywell and produce research that you would be proud of. I would also like to thank my associate supervisor Dr Alex Samarian. I would also like to give a big shout out to the rest of the Polywell crew, Matt Carr, Dave Gum- mersall and Johnson Ren with whom I have enjoyed extensive collaboration and thoroughly enjoyable discussions about all things Polywell. A special thanks to Dave for his collaboration in my first Polywell experiment, whose contributions were the icing on the cake. To my original office mates Colin Tuft and Adam Israel I truly had a blast with you guys. I wish you all the best for the future. The technical staff at the School of Physics have helped me in many ways. Particularly the workshop staff, Mr. Michael Paterson and Mr. Terry Pfeiffer who helped me in designing and machining the Polywells used in this thesis. A particular thanks to Mr Phil Dennis who consulted me on power supply design and checked that my work would not result in death. I would also like to thank the School of Physics administration staff, particularly Ms Eve Teran, Miss Alexis George and Ms Cynthia Kiu who were endlessly supportive in all my administrative needs. Finally to the School of Physics itself which provided me with the Denison Postgraduate Award and allowed me to undertake this PhD program. To my parents, thank you for the support you provided during the early years of my thesis. Finally the biggest thankyou of all to my beautiful and brilliant wife Louise. You have been a constant source of inspiration and support. Without you I would have thrown in the towel and never finished this thesis. Of this, I am sure. As I now come to the close of my PhD work on the Polywell, I am reminded of the introduction to one of my favourite Led Zeppelin songs. Indeed, is this the end or just beginning? Only time will tell. ii Should I fall out of love, my fire in the light To chase a feather in the wind Within the glow that weaves a cloak of delight There moves a thread that has no end. For many hours and days that pass ever soon the tides have caused the flame to dim At last the arm is straight, the hand to the loom Is this to end or just beginning? All of my Love - Led Zeppelin iii Abstract The Polywell is an Inertial Electrostatic Confinement (IEC) device that aims to confine ions at fusion energies. The Polywell uses a virtual cathode in place of a metal grid cathode used in regular IEC devices, in which a high voltage is applied to the grid to accelerate ions to fusion energies and confine them in a spherical geometry. The virtual cathode is produced by confining high energy electrons in a magnetic well by mirror reflections, which produces a potential well. Three orthogonal pairs of coils with antiparallel currents are placed equidistant from the centre of the device, such that the six coils make up the faces of a cube. In this way a magnetic well is produced with a magnetic null at the centre of the device and strong magnetic fields near the coils. Spherically symmetric potential wells are also required in order to maximise the degree of ion focusing attained in the core of the device. The formation of deep, symmetrical potential wells is critical to the functioning of the Polywell and is the major focus of this thesis. This thesis aims to explore how the depth and symmetry of potential wells vary with a number of device parameters. These include injected electron current and electron energy and magnetic field strength. The spacing of magnetic field coils is also investigated. Varying the spacing of the magnetic field coils changes the relative magnetic field strength in the different cusps of the device and hence the electron trapping in these cusps. Electron losses through the cusps represent a major energy loss mechanism and are a major impediment to the potential of the device to eventually reach net fusion energy. The electron trapping is maximised by determining the ideal intercoil spacing. Different sizes of magnetic field coil were used to investigate how increasing the device size improves the electron trapping and potential well formation. It is hypothesized that larger devices are able to trap higher energy electrons and produce deeper potential wells capable of accelerating ions to fusion energies. The scaling experiments with smaller devices are used to estimate the size of device needed to reach fusion energies. In order to investigate the potential formation multiple secondary electron emission capacitive probes (SECP) were constructed. The use of these probes in the Polywell plasma could give a direct measure of the plasma potential and hence the potential well. However, this type of probe has not be shown to be effective in the highly magnetised non-Maxwellian, non-neutral electron plasma found in the Polywell. A planar vacuum diode within a Helmholtz pair is used to test the applicability of a SECP in such a plasma, with magnetic fields up to 0.35 T, and for electron energies of 100 eV-4000 eV. The plasma potential is accurately measured by the probe when the electron Larmor radius is greater than the probe diameter. When the electron Larmor radius is less than the probe diameter, the measured plasma potential iv is underestimated. However, this effect ceases at a finite Larmor radius and the SECP can be used to measure the plasma potential in high magnetic fields using a correction factor. A small Polywell with a 48 mm average coil diameter is tested with central face magnetic fields up to ∼ 0:5 T. The effect of magnetic field coil current and electron injection current and electron energy on the development of potential wells is observed. The electron emission current is varied from 150- 1680 mA and electron energies range between 150-800 V. These device parameters are tested over a much larger range than previously examined. A linear relationship is observed between potential well depth and injection current. A non-linear relationship is observed between potential well depth and magnetic field strength, with further increases to the magnetic field strength having less effect on the well depth. Investigations are made into the effect of the applied magnetic field current on the amount of emitted electrons that are injected into the device. An analytical model is created to estimate the electron confinement time from the measured potential well depth. From these results, an experimentally derived equation for electron confinement time is constructed, based on the experimental parameters of electron energy and coil current. These results are compared to a similar equation derived from a particle orbit simulation. A similar setup is used to again test the effect of magnetic field strength and emission current on the potential well depth. However, in the second experiment the two variables are completely decoupled. A nonlinear relationship is now observed between emission current and potential well depth, with the increases to both variables having diminishing returns on the well depth achieved.
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